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Mathematical Models of Budding Yeast Colony Formation and Damage Segregation in Stem Cells

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Mathematical Models of Budding Yeast Colony Formation and Damage Segregation in Stem Cells Mathematical models of budding yeast colony formation and damage segregation in stem cells Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Yanli Wang, B.S., M.S. Graduate Program in Mathematics The Ohio State University 2017 Dissertation Committee: Dr. Ching-Shan Chou, Advisor Dr. Janet Best Dr. Ghaith Hiary Dr. Wing-Cheong Lo c Copyright by Yanli Wang 2017 Abstract This dissertation consists of two chapters. In Chapter 1, we present a individual-based model to study budding yeast colony development. Budding yeast, which undergoes polarized growth during budding and mating, has been a useful model system to study cell polarization. Bud sites are select- ed differently in haploid and diploid yeast cells: haploid cells bud in an axial manner, while diploid cells bud in a bipolar manner. While previous studies have been focused on the molecular details of the bud site selection and polarity establishment, not much is known about how different budding patterns give rise to different functions at the population level. In this chapter, we developed a two-dimensional agent-based model to study budding yeast colonies with cell-type specific biological processes, such as budding, mating, mating type switch, consumption of nutrients, and cell death. The model demonstrates that the axial budding pattern enhances mating probability at the early stage and the bipolar budding pattern improves colony development under nutrient limitation. Our results suggest that the frequency of mating type switch might control the trade-off between diploidization and inbreeding. The effect of cel- lular aging was also studied through our model. Based on the simulations, colonies initiated by an aged haploid cell show declined mating probability in the early stage and recover as the rejuvenated offsprings become the majority. It was shown that ii colonies initiated by aged diploid cells do not show disadvantage in colony expansion due to the fact that young cells contribute the most to colony expansion. In Chapter 2, we present a continuous population model of transport type to study stem cell aging. Stem cells are important for living creatures in that they generate all specialized tissues and give rise to the entire body at early life stage, and also serve as a repair system to replenish adult tissues while maintaining the stem cell pool for the lifetime of the living creature. Persistent division leads to stem cells suffering from the accumulation of molecular damages, which are commonly recog- nized as drivers of aging. As research on stem cells continues to advance, interesting questions arise as rapidly as new discoveries. How do stem cells respond to internal and external signals and regulate self-renewal and differentiation? How do stem cells cope with damage accumulation and maintain fitness? In this research, we propose a novel model to integrate stem cell proliferation and differentiation with damage ac- cumulation in stem cell aging process. A system of two structured PDEs are used to model stem cells (including all multiple progenitors) and TD cells (terminally differ- entiated cells). It is assumed that cell cycle progression is continuous while division is discrete, and damage segregation takes place at division. Regulations from TD cells and stem cells population are incorporated through negative feedbacks on stem cell proliferation and symmetric division. Aging effect is added through the inhibition from damage accumulation on stem cell proliferation and self-renewal. Analysis and numerical simulations are conducted to study steady state populations and stem cell damage distributions under different damage segregation rules. Our simulations sug- gest that equal distribution of damage between stem cells in symmetric renewal and less damage retention in stem cell in asymmetric division are favorable rules, which iii reduce the death rate of stem cells and increase TD cell populations. But asymmet- ric damage segregation in stem cells leads to less concentrated damage distribution in stem cells population, which may be more stable to sudden increase of damage. Compared to feedbacks solely from TD cells, adding feedbacks from stem cells will reduce oscillations and population overshoot in the process of population convergence to steady state. Moreover, adding the regulation that slows down the proliferation of stem cells with high level of damage and increases their tendency to differentiate can improve the fitness of stem cells by increasing the percentage of stem cells with less damage in the stem cell population. iv Dedicated to my family. v Acknowledgments First I would like to express my deepest gratitude to my advisor Professor Ching- Shan Chou for her patient guidance and constant support through the years. I am grateful to Professors Janet Best, Ghaith Hiary and Wing-Cheong Lo for agreeing to be on my dissertation defense committee. Regarding the dissertation, I thank Professor Hay-Oak Park for discussion and comments on Chapter 1. Special thanks go to Professor Wing-Cheong Lo, for his advice, encouragement, understanding, and conversations throughout all my research projects. It is my pleasure to record my thanks to many friends, Dr. Ting-Hao Hsu, Dr. Jihui Huang, Yongxiao Lin, Dr. Weizhou Sun, and Dr. Xiaohui Wang. I thank the teaching support team members at Ohio State, Cindy Bernlohr (re- tired), Dr. Dan Boros, John Lewis and Debi Stout, for their valuable consultation and resourceful help regarding teaching and beyond. Lastly, I thank my family members, whose love and support give me courage and strength to face and overcome hardships. vi Vita 2008 . .B.S. in Mathematics, Shandong University, Jinan, China 2011 . .M.S. in Mathematics, Shandong University, Jinan, China 2013-2015 . Master of Applied Statistics, The Ohio State University 2011-present . .Graduate Associate, The Ohio State University Fields of Study Major Field: Mathematics Specialization: Applied Mathematics vii Table of Contents Page Abstract . ii Dedication . .v Acknowledgments . vi Vita......................................... vii List of Tables . .x List of Figures . xi Chapter 1: Modeling Budding Yeast Colonies: an Agent-based Approach . .1 1.1 Introduction . .1 1.2 Model description . .6 1.3 Results . 18 1.3.1 Mating type switch frequency controls the trade-off between diploidization and inbreeding . 18 1.3.2 Axial budding pattern in haploid yeast cells facilitates mating 19 1.3.3 Bipolar budding is necessary for a branched colony under limited nutrient . 22 1.3.4 Mating efficiency is lower in aged colonies but colony expan- sion does not depend on the overall age of the colony . 27 1.4 Conclusions and discussions . 30 Chapter 2: Modeling stem cell aging: a multi-compartment continuum ap- proach . 34 2.1 Introduction . 34 2.2 Model Description . 40 2.3 Models with constant parameters . 44 2.3.1 Analytic solution . 46 viii 2.3.2 Analysis of population dynamics . 46 2.4 Models with feedbacks . 51 2.4.1 Feedbacks from TD cells . 53 2.4.2 Feedbacks from stem cells . 63 2.5 Conclusions and discussions . 72 Appendices 76 Appendix A: Supporting Information for Chapter 1 . 76 A.1 Estimation of parameters . 76 A.2 A sample colony generated by a single haploid cell . 80 A.3 Demonstration of minimal covering circles . 81 A.4 Samples of bipolar/random budding colonies under rich/poor nutri- ent conditions . 82 A.5 Numerical methods . 84 A.5.1 Dynamics of agents . 84 A.5.2 Numerical scheme solving the evolution of the nutrient field 85 Appendix B: Supporting Information for Chapter 2 . 86 B.1 Derivation of Equation (2.12) . 86 B.2 Derivation of the limit damage band . 87 B.3 Proof of Proposition 2.1 . 88 B.4 Proof of Proposition 2.2 . 89 B.5 Proof of Proposition 2.3 . 90 B.6 Parameters in the model with feedback from TD cells . 92 B.7 TD cell population and population ratio when β1 = 0:1 and 0:3, see Fig. B.5 . 99 B.8 Estimation of populations in the models with feedbacks from TD cells 99 B.9 Parameters in the model with feedbacks from TD cells and stem cells 103 B.10 Numerical Scheme . 104 Bibliography . 108 ix List of Tables Table Page 1.1 The time of first mating. 21 2.1 The choices of parameters, estimated based on biological evidence and previous modeling works, with details in Appendix B.6. 57 2.2 Death rate of stem cells in steady state under different segregation rules. 59 2.3 Symmetric renewal fraction δ1 in steady state under different segrega- tion rules. 60 2.4 Segregation rules in Fig. 2.9. 63 2.5 The choices of additional parameters, estimated based on biological evidence and previous modeling works, with details in Appendix B.9. 67 2.6 Death rate of stem cells in steady state under different segregation rules. 71 A.1 Parameters used in simulations and their references. 79 B.1 Comparison of initial division fractions. 95 B.2 Comparison of regulation parameters. 96 B.3 Comparison of Hill exponents. 98 x List of Figures Figure Page 1.1 The life cycle of budding yeast. .2 1.2 A schematic of the agent-based model, with the key biological and physical quantities. .7 1.3 Overview of the processes within a single cell cycle. Pd and Pb are the probabilities of cell death and normal budding (axial for haploid cells and bipolar for diploid cells), respectively. Ps is the frequency of mating type switch. Pm is the frequency of successful matings. The simulation stops when the maximal time or the maximal population is attained. .8 1.4 Budding patterns for haploid and diploid cells. Haploid cells bud in an axial manner: both mother and daughter cells have bud sites adjacent to the previous division site.
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